Capacitors are passive, two terminal electrical devices for storing energy in electric fields and are commonly found in electrical and electronic circuits used in a wide variety of applications. They typically comprise a dielectric sandwiched between two generally parallel conductors and store energy in an electric field generated in the dielectric by negative charge accumulated on one of their conductors and positive charge accumulated on the other of their conductors. By way of example, capacitors are used to reduce ripple in voltage provided by power supplies, to multiply voltage in charge pumps, to isolate signal circuits from direct current (DC) signals and voltages, and to filter out noise in signal processing circuits. Capacitors function as snubbers in switching circuits, pulse power sources in weapons systems, and energy storage components in solid state circuits.
Electrical features of a capacitor are characterized by capacitance “C”, which is a coefficient that relates an amount of energy stored in an electric field in the dielectric of the capacitor to voltage between the capacitor conductors. If “E” represents an amount of energy stored in the capacitor for a given voltage difference “V” between the conductors the stored energy is given by an expression E=(½)CV2. An amount of charge “Q” that resides on the conductors is related to V by an expression Q=CV.
Capacitance C is determined by geometric features of the capacitor and permittivity of the dielectric. Assuming that the conductors are parallel planar conductors separated by a distance “d” and have area “A”, and that the relative permittivity of the dielectric is “∈r”, C may be given by an expression C=∈o∈rA/d, where ∈o is the permittivity of free space. In the MKS (meter, kilogram, second) system of units, ∈o=10−9/(36π), d is in meters (m), area A is in square meters (m2) and C is given in Farads (F). A useful figure of merit of a capacitor is its specific capacitance, herein represented by “C*”, which is the capacitor's capacitance per unit volume of the capacitor. The specific capacitance provides an indication of how much space a capacitor occupies in a circuit for an amount of capacitance it provides.
As electronic components and circuits that comprise the components decrease in size and their three dimensional volumes shrink it is generally advantageous that capacitors also shrink and provide increasing specific capacitance. However, as capacitors shrink and their specific capacitances increase, for a given desired range of operating voltages, magnitudes of electric fields generated between their conductors, in their dielectrics, and between their terminals, increase. As a result, it becomes increasingly difficult to configure high specific capacitance capacitors to support the large fields they generate for operating voltage ranges and breakdown voltages required by many applications.
A product of an operating voltage of a capacitor and its specific capacity, may be used to provide a figure of merit for a capacitor that is responsive to both the specific capacitance and operating voltage of the capacitor. The product, hereinafter referred to as a “specific operating charge” Q*, is equal to a charge a capacitor stores at its operating voltage per unit volume of the capacitor. For convenience of presentation, specific operating charge is given below in units of Volts×μF/mm3 (microfarad/cubic millimeter), rather than coulombs per m3 (cubic meter).
Electrolytic capacitors, which comprise a metal terminal typically formed from Aluminum or Tantalum, on which a thin dielectric layer of an oxide of the metal is grown by an electrolytic process, are often used for applications that require high specific capacitance. By way of example, KEMET Electronic Corp markets a 1000 μF (microfarad) Tantalum electrolytic capacitor under the catalog number “T530X108M003AS” for surface mount applications. The KEMET capacitor operates at 2 volts, has dimensions 7.3 mm×4.3 mm×4.3 mm and therefore a specific capacitance equal to about 7.4 μF/mm3, and a specific operating charge equal to about 14.8 V μF/mm3. Whereas electrolytic capacitors provide relatively large capacitances their oxide-metal interfaces are rectifying. As a result they are generally polar capacitors having a positive terminal and a negative terminal and they must be connected to a circuit so that voltage on the positive terminal is always greater than or equal to a voltage on the negative terminal.
Applications that require very high capacitances and high specific capacitances may use electrochemical capacitors, also referred to as, super-capacitors, ultra-capacitors, or electric double-layer capacitors. The electrochemical capacitors comprise electrodes in contact with a liquid or solid electrolyte. As the name “electric double-layer capacitor” implies, these capacitors store energy in electric fields generated between two layers of opposite charge that are separated by very small distances. The charge double-layers may be separated by distances between about 0.3 nm (nanometers) to about 0.5 nm and are formed at the interfaces between the capacitors electrodes and the electrolyte.
As a result of the very small separation distances of the charge layers in their double-layers, electrochemical capacitors may have very large capacitances, and very large specific capacitances. An electrochemical capacitor may have capacitance of hundreds of Farads and a specific capacitance of a few milliFarads per cubic millimeter (mF/mm3). However, their operating voltages are limited by breakdown voltages of their electrolytes, which are typically between 1 and 3 volts and they exhibit relatively large effective series resistance (ESR), which limits their operational frequency bandwidths.
Batteries have structures similar to that of capacitors and generally comprise two terminals coupled respectively to an anode electrode and a cathode electrode that sandwich between them an electrolyte. However, whereas in capacitors materials in the electrodes do not chemically react with material in the electrolyte, in batteries materials in the anode and cathode undergo oxidation and reduction reactions to store electrical energy and deliver stored electric energy to a load.